What is the factorization of the trinomial below?

Question

8x^2-14x-15

Is there a faster way in find the answer instead of subbing all the numbers in?

Answer 1

8x²-14x-15

Product is 8x² × -15 = -120 x² (multiply outer numbers)

and whose

Sum is -14x (inner number).

We try some terms and easily get -20x and 6x.

These are correct since:

• (-20x)(6x) = -120x²
• -20x + (6x) =-14 x

Now write the original expression replacing -14x with  ( - 20x + (6x) ), as follows:

8x²-14x-15= 8x² + (-20x+6x) − 15

We now re-group the right-hand side:

8x² + (-20x+6x) − 15 = (8x² - 20x) +(6x - 15)

Now factor each of the bracketed terms:

(8x² - 20x) +(6x - 15) = 4x(2x - 5) + 3(2x - 5)

On the right-hand side, we notice that each term in brackets is the same, so we can combine them as follows:

4x(2x - 5) + 3(2x - 5) = (2x − 5)(4x + 3)